Multiple choice

A tangent is drawn to a circle from a point $2.6$ cm apart from its center. The length of the tangent is $2.4$ cm, then the diameter of the circle is ?

  1. $\sqrt 5 cm$
  2. $2.5$ cm
  3. $2$ cm
  4. $1$ cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The radius, tangent, and distance to center form a right triangle. r^2 + 2.4^2 = 2.6^2. r^2 + 5.76 = 6.76, so r^2 = 1, r = 1. Diameter = 2r = 2 cm.

AI explanation

By the tangent-secant theorem, the square of the tangent's length equals the square of the distance to the center minus the square of the radius. Substituting the known values gives 2.4 squared equals 2.6 squared minus the radius squared. This simplifies to 5.76 equals 6.76 minus the radius squared, making the radius squared equal to 1 and the radius equal to 1 cm. The diameter is twice the radius, so it is 2 cm.

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